Description

Book Synopsis
The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.

Table of Contents
The Schwarz Principle of Reflection.

The Logarithmic Potential, Balayage, and Quadrature Domains.

Examples of ``Quadrature Identities''.

Quadrature Domains: Basic Properties, 1.

Quadrature Domains: Basic Properties, 2.

Schwarzian Reflection, Revisited.

Projectors from L? (dOmega) to H? (dOmega).

The Friedrichs Operator.

Concluding Remarks.

Bibliography.

Index.

The Schwarz Function and Its Generalization to

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      Book details

      Publisher John Wiley & Sons Inc
      Published 14 April 1992
      ISBN-13 9780471571278
      978-0471571278
      ISBN-10 047157127X
      Also in:
      Mathematics Differential calculus and equations

      Description

      Book Synopsis
      The Schwarz function originates in classical complex analysis and potential theory. Here the author presents the advantages favoring a mode of treatment which unites the subject with modern theory of distributions and partial differential equations thus bridging the gap between two-dimensional geometric and multi-dimensional analysts. Examines the Schwarz function and its relationship to recent investigations regarding inverse problems of Newtonian gravitation, free boundaries, Hele-Shaw flows and the propagation of singularities for holomorphic p.d.e.

      Table of Contents
      The Schwarz Principle of Reflection.

      The Logarithmic Potential, Balayage, and Quadrature Domains.

      Examples of ``Quadrature Identities''.

      Quadrature Domains: Basic Properties, 1.

      Quadrature Domains: Basic Properties, 2.

      Schwarzian Reflection, Revisited.

      Projectors from L? (dOmega) to H? (dOmega).

      The Friedrichs Operator.

      Concluding Remarks.

      Bibliography.

      Index.

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